Higgs mass isn't natural, but maybe it shouldn't be

It’s like a two-headed snake. Cats playing with dogs. Rabbits without baby bunnies. Voldemort’s nose.

It ain’t natural.

In this case, “natural” does not mean the opposite of artificial, like sweeteners or Christmas trees. “Naturalness” is actually a technical term in physics, although there is some confusion about exactly how to define it.

In any event, the Large Hadron Collider’s discovery of the Higgs boson with the mass that it had (roughly 125 times the mass of a proton) has perplexed some physicists because they can’t articulate a “natural” explanation for it.

To get a just a bit more technical, the issue involves what physicists call the “hierarchy” problem. It has to do with particle masses. (Remember, the Higgs particle is the offspring of a field that gives particles their masses.) Naively, it would be natural to expect particles to have masses at roughly the scale of the fundamental quantum unit of mass, known as the Planck mass. It’s calculated by properly combining Newton’s gravitational constant, Planck’s constant and the speed of light in a formula producing a number with the units of mass. And it turns out to be roughly 10 million billion trillion electron volts, or 20 millionths of a gram. By particle physics standards, that’s enormously heavy — physicists variously compare it to the mass of an eyebrow hair, or a flea’s egg, or millions of bacteria.

Obviously, subatomic particles are not that heavy — they’re lighter by a factor exceeding 10 million billion.

There are “natural” ways to explain light particles, but those ways don’t seem to work with the Higgs. Its mass just ain’t natural. Quantum physics provides formulas for calculating what the Higgs mass should be, and the Higgs should be very, very heavy, unless some of the factors entering the calculations cancel each other out. And they have to cancel each other out to an extraordinarily high degree of precision — the technical term for that is “fine tuning.”) Naturalness, to physicists, means no (or very little) fine tuning.

A nice historical illustration of this concept comes from Jonathan Feng, of the University of California, Irvine, in a recent article in the Annual Review of Nuclear and Particle Science. It turns out that Isaac Newton himself articulated the meaning of naturalness in response to a question about how the universe could be static. (In those days, nobody knew the universe was expanding.) If all masses attracted, why wouldn’t everything in the universe be moving closer and closer together? Newton replied that it was indeed a very unnatural state of affairs. A mass would have to be placed precisely at the center of all other masses, attracted equally in all directions, to remain motionless. Achieving such a state, Newton said, would be “fully as hard as to make the sharpest needle stand upright on its point upon a looking-glass.”

Newton’s solution was to suppose that some divine power had established the precisely proper (and finely tuned) initial conditions to sustain a static infinite universe. But that was a supernatural explanation, not a natural one.

In the Higgs case, a prime candidate for a natural explanation was supersymmetry, aka SUSY. SUSY adds a new set of subatomic particles into the mix, one superpartner for each previously known particle. When the presence of the superparticles is accommodated in the equations, the Higgs mass comes out just right — SUSY required it to be less than 130 billion electron volts, and the Higgs weighed in at 125. But that success turned sour because the LHC did not find the SUSY particles that were supposed to be there to keep the Higgs mass so low. Without the SUSY particles, the Higgs mass is not natural at all.

“This is either a challenge to naturalness or a challenge to our ability to construct natural theories,” writes Nathaniel Craig of the Institute for Advanced Study in Princeton, N.J. But it does not, as has been rather widely implied, mean that the SUSY theory is necessarily wrong.

“I do not mean this to say that there is no supersymmetry in nature,” Craig writes. “Rather, I mean that the march of null results suggests that we were mostly wrong about precisely how supersymmetry would appear at the LHC.”

In fact, naturalness is just one of two principles that led to the belief that the LHC would find SUSY. There’s also parsimony, the old Occam’s razor notion of explaining more with less. If you want to explain why, say, five numbers are what they are, your theory shouldn’t require six new numbers. If several numbers are fine-tuned — if you just have to throw up your hands and say you don’t know why they’re what they are — then you don’t know much. But if one or two numbers can explain why all the other numbers are precisely what they are, then you have parsimony.

“We built our expectations for supersymmetry at the LHC on the twin pillars of parsimony and naturalness,” Craig writes. “The null results at the LHC suggest that those two pillars were perhaps not the right foundations.”

It’s true, he says, that the simplest version of SUSY has trouble explaining the LHC’s inability to find SUSY particles. But there are many variations on SUSY under active investigation that have not been ruled out by LHC data (see Feng’s paper for examples). These more complicated forms of SUSY just don’t look so sharp when viewed through the lens of parsimony. On the other hand, if you don’t care so much about naturalness, you can still have the relatively simple SUSY.

An “unnatural” (and to many, unpalatable) explanation for the Higgs mass invokes “anthropic” reasoning. Perhaps the Higgs mass (and other properties of the universe) are not fixed precisely by any theory, but can assume a wide range of values in different regions of the universe (or in different parallel universes). We measure the Higgs mass that we do because that’s the mass in the universe that has properties hospitable to life. Fine tuning is no longer an issue, then; you don’t need to explain why the Higgs mass is low if there would be no life to wonder about it in a universe where the Higgs mass is high.

Of course, many scientists have strong philosophical predispositions against anthropic arguments, just as they have had strong philosophical predispositions favoring naturalness and parsimony. But philosophical predispositions may not be the best guides to deciding whether to jettison a theory or not.

“If the combination of philosophy plus theory is incompatible with observation,” writes Craig, “we should consider the consequences of changing philosophies before we completely discard the theory itself.”